The triad of nuclei that is isotonic is

Options

A. `._(6)C^(14), ._(7)N^(15), ._(9)F^(17)`,
B. `._(6)C^(12), ._(7)N^(14), ._(9)F^(19)`,
C. `._(6)C^(14), ._(7)N^(14), ._(9)F^(17)`,
D. `._(6)C^(14), ._(7)N^(14), ._(9)F^(19)`,

Explanation

To solve the question regarding the triad of isotonic nuclei, we need to understand the concept of isotones. Isotones are nuclei that have the same number of neutrons but different numbers of protons (i.e., they belong to different elements).

Here’s the step-by-step solution:

### Step 1: Understand the definition of isotones
Isotones are defined as nuclei that have the same number of neutrons (N) but different atomic numbers (Z). The number of neutrons can be calculated using the formula:
\[ N = A - Z \]
where \( A \) is the mass number and \( Z \) is the atomic number.

### Step 2: Analyze the options provided
We will analyze each option to find a triad of nuclei that are isotonic.

### Step 3: Calculate the number of neutrons for each option

#### Option A:
1. **Carbon-14 (C)**:
- Mass number (A) = 14, Atomic number (Z) = 6
- Neutrons = \( 14 - 6 = 8 \)

2. **Nitrogen-15 (N)**:
- Mass number (A) = 15, Atomic number (Z) = 7
- Neutrons = \( 15 - 7 = 8 \)

3. **Fluorine-17 (F)**:
- Mass number (A) = 17, Atomic number (Z) = 9
- Neutrons = \( 17 - 9 = 8 \)

Since all three nuclei have 8 neutrons, they are isotonic.

#### Option B:
1. **Carbon-12 (C)**:
- Neutrons = \( 12 - 6 = 6 \)

2. **Nitrogen-14 (N)**:
- Neutrons = \( 14 - 7 = 7 \)

3. **Fluorine-19 (F)**:
- Neutrons = \( 19 - 9 = 10 \)

The neutrons are not the same; hence, this option is eliminated.

#### Option C:
1. **Carbon-14 (C)**:
- Neutrons = \( 14 - 6 = 8 \)

2. **Nitrogen-14 (N)**:
- Neutrons = \( 14 - 7 = 7 \)

3. **Fluorine-17 (F)**:
- Neutrons = \( 17 - 9 = 8 \)

The neutrons are not the same; hence, this option is eliminated.

#### Option D:
1. **Carbon-14 (C)**:
- Neutrons = \( 14 - 6 = 8 \)

2. **Nitrogen-14 (N)**:
- Neutrons = \( 14 - 7 = 7 \)

3. **Fluorine-19 (F)**:
- Neutrons = \( 19 - 9 = 10 \)

The neutrons are not the same; hence, this option is eliminated.

### Conclusion
The only option where all three nuclei have the same number of neutrons (8) is **Option A** (Carbon-14, Nitrogen-15, and Fluorine-17). Thus, the triad of isotonic nuclei is:

**Answer: Option A: Carbon-14, Nitrogen-15, Fluorine-17**